Q: A 2 kg object is moving at 3 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Q: A box is pulled 5 m across a frictionless surface by a constant horizontal force of 10 N. How much work is done by the force?

$$W = Fd = 10 \times 5 = 50\ \mathrm{J}$$

Q: A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Q: A force of 20 N acts at an angle of $$60^\circ$$ above the horizontal and moves an object 4 m horizontally. What is the work done by the force?

$$W = Fd\cos\theta = 20 \times 4 \times \cos 60^\circ = 40\ \mathrm{J}$$

Q: A spring with spring constant $$k = 500\ \mathrm{N/m} is $$compressed by 0.1 m. What is the work done by the spring force during this compression?

$$W = -\frac{1}{2}kx^2$ = -\frac{1}{2} \times 500 \times (0.1)^2$ = -2.5\ \mathrm{J}$$

Q: A 1000 kg elevator descends 12 m at constant speed. What is the total work done by gravity on the elevator?

$$W = mgd = 1000 \times 9.8 \times 12 = 117,600\ \mathrm{J}$$

Q: A sled of mass 50 kg is pulled by a force of 200 N at an angle of $$30^\circ$$ above the horizontal for 10 m. What is the work done by the force?

$$W = 200 \times 10 \times \cos 30^\circ = 1,732\ \mathrm{J}$$

Question 1

Which of the following best describes the principle of conservation of energy?

Accepted Answer

Energy can change forms, but the total energy in a closed system remains constant.

Question 2

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 3

A box is pulled 5 m across a frictionless surface by a constant horizontal force of 10 N. How much work is done by the force?

Accepted Answer

$$W = Fd = 10 	imes 5 = 50\ \mathrm{J}$$

Question 4

Which of the following is NOT a form of energy discussed in the study materials?

Accepted Answer

Magnetic potential energy

Question 5

A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 6

A force of 20 N acts at an angle of $$60^\circ$$ above the horizontal and moves an object 4 m horizontally. What is the work done by the force?

Accepted Answer

$$W = Fd\cos	heta = 20 	imes 4 	imes \cos 60^\circ = 40\ \mathrm{J}$$

Question 7

A spring with spring constant $$k = 500\ \mathrm{N/m} is $$compressed by 0.1 m. What is the work done by the spring force during this compression?

Accepted Answer

$$W = -\frac{1}{2}kx^2$ = -\frac{1}{2} 	imes 500 	imes (0.1)^2$ = -2.5\ \mathrm{J}$$

Question 8

A 1000 kg elevator descends 12 m at constant speed. What is the total work done by gravity on the elevator?

Accepted Answer

$$W = mgd = 1000 	imes 9.8 	imes 12 = 117,600\ \mathrm{J}$$

Question 9

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and can be positive, negative, or zero.

Question 10

A sled of mass 50 kg is pulled by a force of 200 N at an angle of $$30^\circ$$ above the horizontal for 10 m. What is the work done by the force?

Accepted Answer

$$W = 200 	imes 10 	imes \cos 30^\circ = 1,732\ \mathrm{J}$$

Question 11

A 0.4 kg block slides at 2 m/s into a spring with $$k = 750\ \mathrm{N/m}. $$How far is the spring compressed before the block stops?

Accepted Answer

$$\frac{1}{2}mv^2$ = \frac{1}{2}kx^2$ \implies x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{0.4 	imes 2^2$}{750}} = 0.065\ \mathrm{m}$$

Question 12

Which of the following scenarios involves negative work being done?

Accepted Answer

Friction slows down a sliding object.

Question 13

The net work done on an object is equal to:

Accepted Answer

The change in the object's kinetic energy.

Question 14

A force $$F(x) = 3x^2$ (in N) acts on a particle as it moves from x = 0$ to x = 2$ m. What is the work done by this force?

Accepted Answer

$$W = \$$int_0$$^2 3x^2$ dx = [x^3$]_0^2$ = 8\ \mathrm{J}$$

Question 15

A 500 kg elevator is descending at constant speed. The cable exerts an upward force equal to the weight of the elevator. What is the work done by the cable as the elevator descends 10 m?

Accepted Answer

$$W = -mgd = -500 	imes 9.8 	imes 10 = -49,000\ \mathrm{J}$$

Question 16

Which of the following is a correct statement about the usefulness of energy after transformations?

Accepted Answer

Energy can become less useful after transformations, even though it is conserved.

Work and Energy: Concepts, Conservation, and Applications

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